Two sides and the non-included right angle of one right triangle are congruent to the corresponding parts of another right triangle. which congruence theorem can be used to prove that the triangles are congruent?

aas
sss
sas
hl

- HL congruence theorem.

HL theorem or hypotenuse-leg theorem tells that if the hypotenuse and one leg of a right triangle are congruent to the hypotenuse and one leg of another right triangle, then the triangles are congruent.

⇒ If two sides and the non-included right angle of one right triangle are congruent to the corresponding parts of another right triangle then by the HL theorem triangles are congruent.

The answer is (D) HL congruence theorem.

Step-by-step explanation:  Given that the two sides and the non-included right angle of one right triangle are congruent to the corresponding parts of another right triangle.

We are to select the correct congruence theorem from the given options.

Since two sides and one angle is given, so AAS and SSS will not be the correct congruence theorem, because

AAS - two angles and the included side,

SSS - threes sides.

In SAS congruence theorem, we take two sides and the included angle which is not true because the angle given in the question is not included between the two sides.

So, SAS is also not correct.

In HL congruence theorem, we take the right-angles of two right-angled triangles, the hypotenuse and one side. Obviously, the right-angle will not be included between the hypotenuse and one side of both the traingles.

Therefore, HL congruence theorem will be used to prove that the two triangles are congruent.

Thus, (D) is the correct option.

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